(\partial)/(\partial x)(cos^5(x^3y^8))

解

\frac{\partial}{\partial x} (cos^{5} (x^{3} y^{8}))

- 15 x^{2} y^{8} cos^{4} (x^{3} y^{8}) sin (x^{3} y^{8})

解答ステップ

\frac{\partial}{\partial x} (cos^{5} (x^{3} y^{8}))

y

を定数として扱う

連鎖法則を適用:

5 (cos (x^{3} y^{8}))^{4} \frac{\partial}{\partial x} (cos (x^{3} y^{8}))

= 5 (cos (x^{3} y^{8}))^{4} \frac{\partial}{\partial x} (cos (x^{3} y^{8}))

\frac{\partial}{\partial x} (cos (x^{3} y^{8})) = - sin (x^{3} y^{8}) \cdot 3 y^{8} x^{2}

= 5 (cos (x^{3} y^{8}))^{4} (- sin (x^{3} y^{8}) \cdot 3 y^{8} x^{2})

簡素化

= - 15 x^{2} y^{8} cos^{4} (x^{3} y^{8}) sin (x^{3} y^{8})